from pi/2 to 5pi/6  2sinx ranges from 2 to 1

so[2sinx]  is 1         ([1....]=1)

from 5pi/6 to pi 2sinx ranges from 1 to 0

so [2sinx] is 0

from pi to 7pi/6 2sinx ranges from 0 to -1

so [ 2sinx] is -1

from 7pi/6 to 3pi/2 2sinx ranges from -1 to -2

so [2sinx] is -2

 

_{[ pi/2]}^{[ 5pi/6]}  1 +_{[pi ]}^{[7pi/6 ]}     -1 +_{[ 7pi/6]}^{[ 3pi/2]}  -2

 

=-pi/2

 

 

xteremly sory yes there was some mis in cal now the ans is -pi/2